Question

A copper–constantan thermocouple is to be used to measure temperatures

between 0 and 200°C. The e.m.f. at 0°C is 0 mV, at 100°C it is 4.277 mV and
at 200°C it is 9.286 mV. What will be the non-linearity error at 100°C as a
percentage of the full range output if a linear relationship is assumed between
e.m.f. and temperature over the full range?

Answer 1

The non-linearity error at 100°C is 0% of the full range output.

Step-by-step explanation:

To calculate the non-linearity error at 100°C as a percentage of the full range output, we need to compare the actual measured EMF at 100°C to what it would be if the relationship between EMF and temperature were perfectly linear over the full range.

Given the provided data points:

At 0°C: EMF = 0 mV

At 100°C: EMF = 4.277 mV

At 200°C: EMF = 9.286 mV

We can assume a linear relationship between EMF and temperature over the full range:

EMF = a * temperature + b

where 'a' is the slope of the line and 'b' is the y-intercept.

Using the given data points at 0°C and 100°C:

0 mV = a * 0°C + b

4.277 mV = a * 100°C + b

Solving this system of equations, we can find the values of 'a' and 'b'.

From the first equation: b = 0

Substitute b = 0 into the second equation: 4.277 mV = a * 100°C

So, a = 0.04277 mV/°C

Now we can calculate the expected EMF at 100°C using the linear relationship:

EMF_expected = 0.04277 mV/°C * 100°C = 4.277 mV

The actual EMF at 100°C is given as 4.277 mV, which matches the expected value calculated above. This means there is no non-linearity error at 100°C when assuming a linear relationship between EMF and temperature.

Therefore, the non-linearity error at 100°C is 0% of the full range output.